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DON BOSCO SCHOOL, ALAKNANDA : CLASS XI - Assignment
CHAPTER 3 – TRIGONOMETRIC FUNCTIONS
Answer the following:
1. Find the value of
cos(2𝜋+𝜃)𝑐𝑜𝑠𝑒𝑐(2𝜋−𝜃)tan⁡(
3𝜋
+𝜃)
2
9𝜋
sec( 2 +𝜃) cos(4𝜋−𝜃)cot⁡(3𝜋−𝜃)
2. Evaluate cos 15o –sin 15o
3. If cosα =
13
14
1
π
7
3
⁡and⁡cosβ = where α and β are acute angles, show that α − β =
4. The circular measures of two angles of a triangle are ½ and 1/3 , find the third angle in
[ ans : 132o 16’ 22’’ ]
English system
5. A circular wire of radius 3 cm is cut and bent so as to lie along a circle of radius 48cm.
Find the angle subtended by the wire at the centre of the circle [ans : 22.5o]
[ ans: 100o]
6. Find the angle between the hands of a clock at 7:20 P.M.
7. If tan 𝑥 =⁡
𝑚
𝑚−1
𝑎𝑛𝑑 tan 𝑦 =⁡
1
2𝑚−1
, 𝑝𝑟𝑜𝑣𝑒⁡𝑡ℎ𝑎𝑡⁡𝑥 − 𝑦 =
𝜋
4
8. If sec x + tan x = 4 , find sin x and cos x. Also find the quadrant in which x lies.
[ ans : sin x = 15/17 , cos x == 8/17 , First ]
9. If 𝑠𝑖𝑛𝛼 + sin 𝛽 = 𝑎, 𝑐𝑜𝑠𝛼 + cos 𝛽 = 𝑏, 𝑝𝑟𝑜𝑣𝑒⁡𝑡ℎ𝑎𝑡 ⁡⁡⁡sin(𝛼 + 𝛽) =
𝑎𝑛𝑑 cos(𝛼 + 𝛽) =
𝑏2 −𝑎2
𝑏2 −𝑎2
10. If tan A + cot A = 2, then find tan100A + cot100A
11. Prove that
cos2xcos3x−cos2xcos7x+cosx⁡cos10x
sin4xsin3x−sin2xsin5x+sin4xsin7x
12. Prove that tan
13. Prove that cos
𝜋
20
2𝜋
7
tan
3𝜋
20
+cos
tan
4𝜋
7
5𝜋
20
tan
+cos
7𝜋
20
6𝜋
7
tan
=−
1
2
9𝜋
20
[ans : 2 ]
= 𝑐𝑜𝑡6𝑥𝑐𝑜𝑡5𝑥
=1
2𝑎𝑏
𝑎2 +𝑏2⁡
14. Prove that sin 10 o sin 50o sin 70 o =
1
8
15. Prove that cos10o cos 30o cos 50o cos 70 o =
16.Prove that
sin⁡(𝐵−𝐶)
𝑐𝑜𝑠𝐵𝑐𝑜𝑠𝐶
17.If cosx +cosy =
18.Prove that
19.Prove that
+
1
2
sin⁡(𝐶−𝐴)
𝑐𝑜𝑠𝐶𝑐𝑜𝑠𝐴
+
sin⁡(𝐴−𝐵)
=0
𝑐𝑜𝑠𝐴𝑐𝑜𝑠𝐵
and sinx+siny =
1
4
3
16
𝑥+𝑦
𝑝𝑟𝑜𝑣𝑒⁡𝑡ℎ𝑎𝑡 tan(
2
1
) =⁡2
√2 + √2 + √2 + 2𝑐𝑜𝑠8𝑥 = 2𝑐𝑜𝑠𝑥
sinx+sin2x
1+cosx+cos2x
= tanx
20.Prove that cos 5x = 16cos 5 x -20 cos 3 x +5cosx
21.Solve the equation cosx + sin x = cos2x + sin2x
22.Find all values of A between 0o and 720o which satisfy the equation
2 cos2A -5cosA + 2 = 0
[ans : 60 o, 300 o, 420 o, 660 o]
𝑥
𝑥
−3
⁡2
2
5
23.Find the value of sin2x, sin , cos2x, cos if, cos x =
24.Find the principal and general solution of
(a) 2sinx + 1 = 0
(b) sin x + cos x=0
25.Find the general solutions for the following
a) sin 2x + sin4x + sin6x = 0
b) 2cos2x + 3sinx = 0
c) cos x + cos3x = 2 - 4sin2x
d) cos x – sin x =
1
√2
e) √2 sec x + tan x = 1
* * *
, x lies in third quadrant.